Earlier quoted context omitted.
Internationalization is a valid point, but I'm not too choked up about my witch doctor not being allowed to perform open heart surgery. Besides, he would probably rather prescribe me water or stick needles in me instead.
Sarcasm aside, you're missing the point. Why isn't it sufficient to regulate the title 'Doctor' without preventing other practitioners from practicing? People who wanted a traditional medical practitioner would be protected, and those who were willing to take more risk would have the choice.
The staggering amount of money that do get paid to quacks selling stuff that is proven not to work show us very clearly that informed choice is largely a fantasy when dealing with the general public.